Question

Assertion :Statement - 1 f (x) $=$ |x| cos x is not differentiable at x $=0$ Reason: Statement - 2 Every absolute value functions are not differentiable.

• A. Statement-1 is True, Statement-2 is True;
  Statement-2 is a correct explanation for
  Statement-1.
• B. Statement-1 is True, Statement-2 is True;
  Statement-2 is NOT a correct explanation
  for Statement-1
• C. Statement-1 is True, Statement-2 is False
• D. Statement-1 is False, Statement-2 is True

Answer 1

The correct option is C Statement-1 is True, Statement-2 is False

$S_1:$Function $f\left(x\right)=|x|cosx$ is not differentiable at $x=0$ because

$RHD:\underset{x\to 0^{+}}{lim}f\left(x\right)=1$ and $LHD:\underset{x\to 0^{-}}{lim}f\left(x\right)=-1$

So, statement $1$ is true.

$S_2:e.g.|x^2|$ is differentiable. Hence statement $2$ is false.